An overdraft fee is the $30 or so you pay when you spend more than you have in a checking account. If you use your debit card to buy a $2 cup of coffee with $0 in your account, the transaction is often approved. In essence, the bank lends you the money, but they charge you an overdraft fee for doing so.
Overdraft fees create nice income streams for banks, but consumers hate them. Most people don't even know that their account has an "overdraft protection" program - meaning that your $2 cup of coffee can cost $32. Some banks strategically process transactions in a way that maximizes overdraft fees.
Regulators are investigating how to improve things. The most likely approach at this point seems to be making the programs "opt in" so that you have to ask for the feature when you open an account.
If you don't like the idea of paying $30 each time you overdraw your account, you have a few options. First, balance your checking account so you know how much you can afford to spend. You can also use an overdraft line of credit, which generally costs less than a fee for each overdraft.
Further reading:

